%\tikzstyle{p6}=[p,double]
{
\begin{figure}[t]
\begin{center}
\pgfdeclarelayer{background}
\pgfdeclarelayer{inbetween}
\pgfsetlayers{background,inbetween,main}
\begin{tikzpicture}%[thick,scale=0.65, every node/.style={scale=0.65}]
\tikzstyle{link}=[-,black,thick,auto,bend angle=70,bend left]
\tikzstyle{arc}=[draw=black,rectangle,rounded corners,fill=lightgray,font=\normalsize]
\tikzstyle{arcNeighborhoodZ}=[semitransparent,very thick,draw=black,densely dotted,rectangle,rounded corners]
\tikzstyle{arcNeighborhoodZ1}=[arcNeighborhoodZ,dashed]
\small 
\node[b]  (v0)  at (90:2cm)                      {$v_{0}$};
\node[v]  (v1)  at (90-360/12:2cm)                {$v_{1}$};
\node[v]  (v2)  at (90-2*360/12:2cm)               {$v_{2}$};

\node[b]  (v3)  at (90-3*360/12:2cm)               {$v_{3}$};
\node[v]  (v4)  at (90-4*360/12:2cm)               {$v_{4}$};
\node[v]  (v5)  at (90-5*360/12:2cm)               {$v_{5}$};

\node[b]  (v6)  at (90-6*360/12:2cm)               {$v_{6}$};
\node[v]  (v7)  at (90-7*360/12:2cm)                 {$v_{7}$};
\node[v]  (v8) at (90-8*360/12:2cm)                {$v_{8}$};

\node[b]  (v9) at (90-9*360/12:2cm)                {$v_{9}$};
\node[v]  (v10) at (90-10*360/12:2cm)               {$v_{10}$};
\node[v]  (v11) at (90-11*360/12:2cm)                {$v_{11}$};


\draw[link] (v0) to (v1);
\draw[link,bend left] (v0.north east) to (v2);
\draw[link] (v0) to (v3);
\draw[link] (v0) to (v11);
\draw[link] (v0) to (v10);

\draw[link] (v3) to (v4);
\draw[link] (v3) to (v5);
\draw[link] (v3) to (v6);
\draw[link] (v3) to (v2);
\draw[link] (v3) to (v1);

\draw[link] (v6) to (v7);
\draw[link] (v6) to (v8);
\draw[link] (v6) to (v9);
\draw[link] (v6) to (v5);
\draw[link] (v6) to (v4);

\draw[link] (v9) to (v10);
\draw[link] (v9) to (v11);
\draw[link] (v9) to (v0);
\draw[link] (v9) to (v8);
\draw[link] (v9) to (v7);

\begin{pgfonlayer}{background}
  \node[arcNeighborhoodZ,fit=(v9) (v10) (v11) (v8) (v7) (v6) (v0),label={[yshift=1.30cm,font=\normalsize]below:$$},yshift=-0.1cm,scale=1.05,blue,fill=blue!40,pattern=north west lines,pattern color=blue] (C0) {};
  \node[arcNeighborhoodZ1,fit=(v3) (v0) (v1) (v2) (v4) (v5) (v6),label={[xshift=1.35cm,font=\normalsize]left:$$},scale=1.05,red,fill=red!70,pattern=north east lines,pattern color=red] (C1) {};
\end{pgfonlayer}
\end{tikzpicture}
\end{center}
\caption{The Lower Bound Graph of Theorem~\ref{thm:MCDS-ST-lowerbound} for $n=12$ and diameter $2$. Bridge vertices are marked by a double frame. The shaded regions represent two bridge clusters that partition the vertices into edge-disjoint sets.}
%  The blue dotted rectangles form $H_Z$ and the red dashed rectangles correspond to $H_{Z'}$.}
\label{fig:lbGraph}
\end{figure}
}
